mu.f

50 lines · 1 definitions · on GitHub (7be4133)

Python version: mu.py, 46 lines, on the right (switch to Python above the code).

Variables on this page (4)

amuenv, cgas, xenv, zenv

Purpose

Computes the gas's mean molecular weight terms for the equation-of-state routines: the ions' contribution AMU, the free electrons' contribution EMU, and RMU $= \mathcal{R}\,(\mathrm{AMU}+\mathrm{EMU})$.

How it fits

Inputs: $T$, $P$, $\rho$ (D), $X$, $Z$, and BETA (probably the ratio of gas to total pressure, as the name suggests); the envelope composition and its AMUENV from COMP_MOD; the gas constant CGAS from CONSTANTS_MOD.
Who calls it: the equation-of-state routine OEQOS06 (at rp_1 also MEQOS, OEQOS and OEQOS01, removed since rp_1).
Outputs: AMU, EMU, RMU.
Modules: COMP_MOD, CONSTANTS_MOD. The unused /CTLIM/, /CONST1/ and /CCOUT2/ of rp_1 are no longer declared.

The method

Ions. If $X$ and $Z$ differ from the envelope's by less than $10^{-5}$ in total, AMU = AMUENV. Otherwise the change is added species by species, with "excess Z (metals) … in the form of carbon(12)": $$\mathrm{AMU} = \mathrm{AMU_{env}} + \frac{\Delta X}{1.008} + \frac{\Delta Y}{4.004} + \frac{\Delta Z}{12.016},\qquad \Delta Y = -(\Delta X + \Delta Z),$$ (the weights ATOMWT are 0.9921, 0.24975 and 0.08322, i.e. $1/A$; a fourth, ATOMWT(4) $= 0.4995$ ($2/4.004$), is set but never read: unused? line 29 ↗). So AMU is the number of ions per unit mass in units of $1/m_u$, the inverse of the ions' mean molecular weight.

Question 1 (lines 40–43 ↗). Carbon for the metals. The comment says excess metals are carbon, which suits helium-burning regions. Is this still the intended approximation for metal changes from settling, where the excess metals are a mixture with a larger mean $A$?
Electrons. From the gas pressure, $\beta P = \rho\,\mathcal{R}\,T\,(\mathrm{AMU}+\mathrm{EMU})$, so $$\mathrm{EMU} = \mathrm{AMU}\left(\frac{\beta P}{\rho\,T\,\mathcal{R}\,\mathrm{AMU}} - 1\right),\qquad \mathrm{RMU} = \mathcal{R}\,(\mathrm{AMU}+\mathrm{EMU}) = \frac{\beta P}{\rho T}.$$

Definitions

subroutineMU

lines 6–50 · GitHub

Uses modules COMP_MOD, CONSTANTS_MOD

Called by OEQOS06

Change log

The changes since rp_1

Changed since rp_1. Declarations only: COMMON blocks to modules, IMPLICIT NONE; its callers other than OEQOS06 are removed.

1C 2C 3C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 4C MU 5C$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ 6 SUBROUTINE MU(T,P,D,X,Z,RMU,AMU,EMU,BETA) 7C 10/14/26 MHP via Claude 8C code changed to convert COMMON/COMP/ into COMP_MOD. 9 USE COMP_MOD 10C 10/14/26 MHP via Claude 11C code changed to convert COMMON/CONSTANTS/ into CONSTANTS_MOD. 12 USE CONSTANTS_MOD 13C 10/20/26 MHP via Claude 14C code changed to replace implicit typing with IMPLICIT NONE and 15C explicit declarations. 16 IMPLICIT NONE 17 REAL*8 AMU,ATOMWT,BETA,D,DFX1,DFX12,DFX4,EE,EMU,P,RMU,T,X,Z 18 19 20 DIMENSION ATOMWT(4) 21C 10/13/26 MHP via Claude: removed the unused COMMON/NMLPAR/ declaration 22C (no member referenced here; residue of the obsolete-option removals). 23C 10/13/26 MHP via Claude 24C code changed to drop COMMON/CTLIM/, declared here but never used. 25C 9/25/26 MHP via Claude 26C code changed to merge COMMON/CONST/, COMMON/CONST1/, COMMON/CONST2/, 27C and COMMON/CONST3/ into a single COMMON/CONSTANTS/ 28C DATA NZP1/12/ 29 DATA ATOMWT/0.9921D0,0.24975D0,0.08322D0,0.4995D0/ 30 SAVE 31 32C SET UP FRACTIONAL ABUNDANCES 33 DFX1 = (X - XENV) 34 DFX12 = (Z - ZENV) 35 IF(DABS(DFX1) + DABS(DFX12) .LT. 1.0D-5) THEN 36C USE ENVELOPE ABUNDANCES 37 AMU = AMUENV 38 ELSE 39 DFX1 = DFX1*ATOMWT(1) 40 DFX12 = DFX12*ATOMWT(3) 41 DFX4 = (XENV+ZENV -X-Z)*ATOMWT(2) 42C ASSUME EXCESS Z(METALS) IS IN THE FORM OF CARBON(12) 43 AMU = AMUENV + DFX1 + DFX4 + DFX12 44 ENDIF 45 EE=((BETA*P)/(D*T*CGAS*AMU))-1.0D0 46 EMU=EE*AMU 47 RMU=CGAS*(AMU+EMU) 48 49 RETURN 50 END

1"""Python version of mu.f (YREC 7be4133): the ions' and electrons' 2mean-molecular-weight terms for the equation of state.""" 3 4from pyrec import comp_mod 5from pyrec import constants_mod 6 7# DATA ATOMWT: 1/A for H, He4 and C12 (excess metals), and 2/4.004, 8# unused in the Fortran too (index 0 unused; Fortran line 29). 9ATOMWT = (0.0, 0.9921, 0.24975, 0.08322, 0.4995) 10 11 12def mu(t: float, p: float, d: float, x: float, z: float, rmu: float, amu: float, emu: float, 13 beta: float) -> tuple[float, float, float]: 14 """Compute the ions' term amu (AMUENV corrected for the change of X and 15 Z, excess metals as carbon), the electrons' term emu from the gas 16 pressure beta*p, and rmu = CGAS (amu + emu). 17 18 Translates: mu.f#MU (7be4133) 19 20 Arguments: t, p, d (rho), x, z and beta; rmu, amu and emu are passed in 21 with any value. 22 23 Returns (rmu, amu, emu). 24 25 """ 26 27 cgas = constants_mod.cgas 28 29 # The ions' term (Fortran lines 33–44). 30 dfx1 = x - comp_mod.xenv 31 dfx12 = z - comp_mod.zenv 32 if abs(dfx1) + abs(dfx12) < 1.0e-5: 33 # The envelope's abundances. 34 amu = comp_mod.amuenv 35 else: 36 dfx1 = dfx1 * ATOMWT[1] 37 dfx12 = dfx12 * ATOMWT[3] 38 dfx4 = (comp_mod.xenv + comp_mod.zenv - x - z) * ATOMWT[2] 39 # Question (see the page): excess Z (metals) taken as carbon 12. 40 amu = comp_mod.amuenv + dfx1 + dfx4 + dfx12 41 42 # The electrons' term from the gas pressure (Fortran lines 45–47). 43 ee = ((beta * p) / (d * t * cgas * amu)) - 1.0 44 emu = ee * amu 45 rmu = cgas * (amu + emu) 46 return rmu, amu, emu